Verifying Chemical Reaction Network Implementations: A Pathway Decomposition Approach.*Seung Woo Shin, Chris Thachuk, Erik Winfree.
What does it mean for two chemical reaction networks to be logically
equivalent? The answer is not as obvious as it may seem -- in fact,
we still can't give a fully satisfactory answer. There seem to be
many possible notions one could entertain, each with its own strengths
and weaknesses. Here we present a refinement of the ideas from Seung Woo's
Masters Thesis that focus on the smallest coherent sequences of
reactions out of which all other sequences can be built. A strength
of the theory is that it can handle the "delayed choice" phenomenon,
wherein a single species in a molecular implementation has already
committed to participation in a reaction, but not yet fully committed
to exactly which one. Combined with bisimulation ideas from Qing Dong's
Masters Thesis, we hope that this theory can address most, if not
all, methods to implement chemical reaction networks using DNA strand
displacement systems -- and perhaps more.
[ article in Theoretical Computer Science
(30 pages, 2018):
PDF, 2.0 MB. ]
[ arXiv preprint v2
(40 pages, May 2017):
PDF, 718 KB. ]
[ arXiv preprint v1
(21 pages, November 2014):
PDF, 365 KB. ]
[ Verification of Engineered Molecular Devices and Programs (VEMDP)
(23 pages, June 2014):
workshop article, 298 KB ]
[ Note: The VEMDP version introduces a notion of "futile loops", not present in the MS thesis theory. The arXiv and TCS versions revert to the theory without futile loop elimination, due to a difficulty proving that our basis-finding algorithm terminates. The proof of Theorem B.1 in the VEMDP version is false as stated. ]

Inferring Parameters for an Elementary Step Model of DNA Structure Kinetics with Locally Context-Dependent Arrhenius Rates.*Sedigheh (Nasim) Zolaktaf, Frits Dannenberg, Xander Rudelis, Anne Condon, Joseph M. Schaeffer, Mark Schmidt, Chris Thachuk, Erik Winfree
Models that capture a substantial fraction of the known thermodynamics
of multistranded DNA molecules at the analytically-tractable secondary
structure level, such as NUPACK, have proven
invaluable for the analysis of both biological and artificial nucleic
acid systems. Extending such models to predict the kinetics of
secondary structure rearrangements and interactions between molecules,
as done for example in the Multistrand
simulation, has the potential to address a wider range of phenomena.
However, thermodynamics does not dictate kinetics -- there is an
infinite family of kinetic models that are perfectly consistent with
any given thermodynamic model -- and therefore the accuracy of naive
kinetics models is limited. Here, we propose a parameterization of
multistranded secondary structure kinetics that is based on the
Arrhenius model for elementary base-pairing changes, and we prototype
a Bayesian Markov Chain Monte Carlo (MCMC) inference method to obtain
an ensemble of improved parameter sets -- resulting in markedly increased
accuracy when evaluated on a database of experimentally-measured
kinetics rates culled from the literature.
[ DNA Computing and Molecular Programming (DNA23) proceedings,
Lecture Notes in Computer Science
(LNCS), Volume 10467, August 2017,
pp 172-187
(16 pages) pdf, 695 KB. ]

A General-Purpose CRN-to-DSD Compiler with Formal Verification, Optimization, and Simulation Capabilities.*Stefan Badelt, Seung Woo Shin, Robert F. Johnson, Qing Dong, Chris Thachuk, Erik Winfree.
What does it mean to compile to molecules? To some, this just means
that a computer was used design the molecules, somehow. To others, a
more rigorous process is implied: that the intended design is
specified by a "high level" formal language, and that a systematic
process is used to translate the design into the "low level" molecular
construction. Here, we go further: the high-level specification
language and the low-level implementation language must each have a
semantics -- that is to say, the intended/expected behavior of
a given system must be well-defined based on its description -- and
more importantly, the behavior of the implementation produced by the
compiler must come with a guarantee that it is effectively the same as the specification. These
features are prototyped by the
Nuskell
compiler, which translates formal chemical reaction networks into
domain-level DNA strand displacement systems.
[ DNA Computing and Molecular Programming (DNA23) proceedings,
Lecture Notes in Computer Science
(LNCS), Volume 10467, August 2017,
pp 232-248
(17 pages) pdf, 1.0 MB. ]

Physical principles for DNA tile self-assembly.*Constantine G. Evans and Erik Winfree
We do our best to provide a gentle but solid introduction to some key
physical principles for DNA tile self-assembly, including algorithmic
growth, error rates, proofreading, and nucleation. We discuss how an
understanding of these issues allows one to navigate from abstract
models of tile assembly, such as the aTAM, to more realistic models of
tile assembly, such as the single-crystal kTAM and the mass-action
kTAM. Finally, we outline a "unified" model of tile self-asssembly
that helps clarify the relationships between different levels of
abstraction.
[
Chemical Society Reviews, DOI:10.1039/C6CS00745G
(22 pages, May 2017):
article, 4.9 MB. ]

"To see a World in a Grain of Sand / And a Heaven in a Wild Flower" -- William Blake.

And so he looked at a tiny bubble
bursting on the surface of an infinite ocean.
Within it, molecules, their world torn asunder.
And in that vigor,
and in that endless churning,
the origin of life.
We followed him deep into this vision.

Universal Computation and Optimal Construction in the Chemical Reaction Network-Controlled Tile Assembly Model.*Nicholas Schiefer and Erik Winfree
The abstract chemical reaction network (CRN) model allows for the
specification of complex dynamical behaviors in a well-mixed solution.
CRN programs have a systematic implementation as DNA strand
displacement cascades. The abstract tile assembly model (aTAM) allows
for the specification of complex self-assembly processes within a
single growing crystal. aTAM programs have a systematic
implementation as DNA tile sets. The CRN-TAM provides a "minimal"
integration of these two models, allowing CRN reactions to produce
tiles, and allowing tile assembly steps to send signals back to the
CRN. Although a compelling implementation is not yet available, we
show that the CRN-TAM can do things neither previous model can do
alone -- in particular, we show that concise CRN-TAM programs can
("optimally") construct arbitrary algorithmically-defined objects,
without the sometimes-dramatic scale-up required in the aTAM.
[ DNA Computing and Molecular Programming (DNA21) proceedings,
Lecture Notes in Computer Science (LNCS), Volume 9211, July 2015, pp 34-54
(21 pages) pdf, 432 KB ]

Niranjan's PhD Thesis:
Programming chemical kinetics: engineering dynamic reaction networks with DNA strand displacement.*
245 pages. California Institute of Technology. Submitted June 2015. Niranjan Srinivas. Thesis advisor: Erik Winfree.
A flute transforms a steady flow of air into an oscillation, a note, a tune.
But can a test tube of molecules sing? Yes -- many chemical oscillators are known, transforming a steady decrease of chemical potential into
wildly swinging concentrations.
One can make a fair argument -- in theory -- that chemical reaction networks can do far more than sing: they can compute, control, and even think.
Niranjan has taken a major step in showing that what is possible in theory may indeed be possible also in practice,
applying a systematic approach to compile abstract chemical reaction networks into enzyme-free systems of interacting DNA molecules.
The specific system he demonstrated is, in fact, a simple oscillator, but the method is general.
Niranjan's thesis won Caltech's 2015 Demetriadis-Tsafka-Kokkalis Prize for Nanotechnology.
[ PhD thesis, 15 MB;
Caltech ETD.]

Verifying polymer reaction networks using bisimulation.*Robert Johnson and Erik Winfree.
Formally, discrete chemical reaction networks (CRNs) have a finite
number of species, but an infinite number of states -- the numbers of
molecules in a test tube is unbounded. The point is, this can make it
hard to verify that a proposed molecular implementation (a big
complicated CRN) is really doing the job it was designed to do (a
smaller simpler CRN). Nonetheless, a method based on Milner's notion
of bisimulation in concurrency theory was developed in Qing Dong's
Masters Thesis. When considering chemical systems involving
polymers of potentially unbounded length, such as the DNA, RNA, and
protein polymers in the central dogma of molecular biology, then the
number of possible species becomes infinite as well. The point is,
the extra infinities can make implementations of polymer reaction
networks (PRNs) even harder to verify. And yet, by extending the
bisimulation ideas, it can (at least sometimes) be done!
[ Verification of Engineered Molecular Devices and Programs (VEMDP)
(15 pages, June 2014):
workshop article, 798 KB ]

Constantine's PhD Thesis:
Crystals that count! Physical principles and experimental investigations of DNA tile self-assembly.*
91 pages. California Institute of Technology. Submitted June 2014. Constantine G. Evans. Thesis advisor: Erik Winfree.
Counting is among the most fundamental computing primitives. One
might say that clocks made of gears and springs -- and astronomical
calculators such as the Antikythera mechanism of 100 BC -- were the
logical precursors of more powerful computing machines like Babbage's
difference engine and even the mechanical cash registers that were used for
counting customers' purchases through the middle of the twentieth
century. Biology, too, uses clocks and counters in a variety of forms:
to step through the cell cycle, to grow each human a full set of 24 ribs,
to make sure that no duckling gets left behind. How
small, and how simple, can a counter be? Constantine has coaxed a set
of 22 DNA molecular tiles to
count
to 31, in binary, as they self-assemble into a
roughly 2 x 80 x 900 nanometer crystal. This must be the precursor to something!
[ PhD thesis, 26 MB;
Caltech ETD.]

On the biophysics and kinetics of toehold-mediated DNA strand displacement.*Niranjan Srinivas, Thomas E. Ouldridge, Petr Šulc, Joseph M. Schaeffer, Bernard Yurke, Ard A. Louis, Jonathan P. K. Doye, and Erik Winfree.
Toehold-mediated DNA strand displacement is at the heart of many
dynamic DNA nanotechnology devices. And it works much much better
than we thought it ought to. So we asked why? It all comes down to
the relative rates of bimolecular collisions, zipping and fraying of
the double-helix, branch migration steps -- and a previously unknown
thermodynamic cost for branch migration intermediates. So now we can
say that toehold-mediated DNA strand displacement works just about as
well as it should. And we have insights about how to make it work better yet.
[ Nucleic Acids Researchdoi: 10.1093/nar/gkt801 (18 pages, September 9, 2013):
article, 5.8 MB and
supp. info., 1.8 MB ]

DNA Sticky End Design and Assignment for Robust Algorithmic Self-assembly.*Constantine G. Evans and Erik Winfree.
Theories of the logic and kinetics of algorithmic self-assembly make
many idealizations that eliminate complexities and clarify essential
insights. But those complexities are still there when one tries to
create self-assembling systems in the laboratory. Which ones are most
important, what effects do they have, and how can one design molecules
and systems to minimize assembly errors? Examining these questions from both biophysical
and combinatorial angles lead us to a
DNA sequence design algorithm that may perform orders of magnitude
better than previous methods.
[ DNA Computing and Molecular ProgrammingLNCS 8141: 61-75 (2013) (15 pages, September, 2013):
article, 821 KB ]
[ Code can be found here. ]

Rizal's PhD Thesis:
Non-equilibrium Dynamics of DNA Nanotubes. *
218 pages. California Institute of Technology. Submitted March 2011, final revision August 2013. Rizal F. Hariadi. Thesis advisor: Erik Winfree; co-advised by Bernard Yurke.
What can Physics tell us about Life? It's not easy to say, as physics
thrives on simplicity, while biology seems to thrive on complexity.
But behind any complex phenomenon lies a simple set of driving
principles, we like to think. In his thesis, Rizal explores some of
the most fundamental principles underlying cellular function -- the
self-organization and dynamical behavior of filamentous polymers such
as those in the cellular cytoskeleton -- by designing, synthesizing,
and quantitatively characterizing DNA nanotubes that self-assemble,
grow, shrink, fragment, and (almost) exhibit treadmilling. In these lifeless pieces we see
fragments of the soul of life.
[ PhD thesis, 27 MB
(better @ 106 MB);
Caltech ETD.]

Sungwook's PhD Thesis:
Beyond Watson and Crick: Programming the Self-Assembly and Reconfiguration of DNA Nanostructures Based on Stacking Interactions. *
144 pages. California Institute of Technology. Submitted May 2013. Sungwook Woo. Thesis advisor: Paul W.K. Rothemund.
Central to DNA nanotechnology is the Watson-Crick base pair. The
exquisite specificity, predictable strength, and combinatorial
diversity of hybridization reactions based on complementary DNA
sequences is what enables us to create sophisticated molecular
programs. But what other bases for complementary binding interactions
might there be? Might we be able to construct a new type of bonding
with the specificity and combinatorial diversity of DNA hybridization,
but which has new and different properties, perhaps allowing for
easier reconfiguration of self-assembled nanomachine parts? In his
PhD thesis, Sungwook starts from the simple observation that DNA
origami stick together at their edges via blunt-end stacking, and
constructs and studies a new system for combining origami based on
binary- and shape-coded stacking interactions. Sungwook applies
stacking interactions towards two different goals: the creation of
large two-dimensional origami crystals on surfaces, and the
origanization of expanding protein filaments to create large-scale
self-assembled geometries. Just as strand displacement enabled a whole
host of molecular programs which were unavailable to simple
equilibrium DNA hybridization, perhaps programmable stacking bonds will enable
a class of new molecular programs which undergo large scale
geometric rearrangement.
[ PhD thesis, 46 MB
(better @ 82 MB);
Caltech ETD.]

Active Self-Assembly of Algorithmic Shapes and Patterns in Polylogarithmic Time.*Damien Woods, Ho-Lin Chen, Scott Goodfriend, Nadine Dabby, Erik Winfree, and Peng Yin.
DNA nanotechnology provides the tools for engineering ``smart''
molecular motors that not only move from place to place, but can
change their actions based on sensing molecules nearby. Molecular
robots, if you will. But don't imagine a single molecular robot.
Imagine a swarm of them. Walking on top of each other like bees or
ants. What power is there in numbers? What power in the ability to
move? On top of one another? Here we develop a theoretical model --
with roots in algorithmic tile self-assembly and L-systems and graph
automata -- that can be used to explore what systems of interacting
molecular robots can accomplish. As a hint of what's to come, here we
examine the fabrication task: build an algorithmically-specified
object. We show that our theoretical molecular robots (called
``nubots'') can fabricate objects exponentially faster and more
compactly than can be done by passive self-assembly systems such as
tile assembly.
[ Pre-publication draft on arXiv:
arXiv:1301.2626v1article, 5.1MB (39 pages). ]
[ Presented
at ITCS 2013: Innovations in Theoretical Computer Science. Berkeley, California, pages 353-354, January 10-12, 2013.]
[ Keynote slides from a presentation at SODA 2014.]

Qing's MS Thesis: A bisimulation approach to verification of molecular implementations of formal chemical reaction networks.*
49 pages. SUNY Stony Brook. Submitted December 2012. Qing Dong. Thesis co-advisors: Steven Skiena and Erik Winfree.
Looking at the world through rose-colored glasses doesn't make
everything go right when it is destined to go wrong. That's exactly
why it can be used as a technique to verify whether a designed system
of molecules -- as described by a detailed and complicated model -- is
a correct implementation of the simple and abstract reaction network
that you wanted to create. If you can find a mathematical
interpretation (the "glasses") that "colors" every molecular species
in the implementation, such that every reaction in the detailed model
"looks like" a reaction in the abstract specification, then you're
good to go. Roughly. Read the thesis for many subtleties.
[ thesis, 394KB;
SUNY Stony Brook thesis depository (not yet up).
]
Note that this is a different approach to the same problem tackled in
Seung Woo
Shin's thesis. Both approaches have their merits!
[Tar archive of Nuskell, the CRN compiler and verifier: Qing's thesis version combined with Seung Woo's code base.]

Ensemble Bayesian Analysis of Bistability in a Synthetic Transcriptional Switch.*Pakpoom Subsoontorn, Jongmin Kim, Erik Winfree.
To attain complexity, one must first master simplicity. That's been
the mantra for much of our research engineering cell-free biochemical
circuits. Previously we developed in vitro transcriptional
systems as a bare-bones model of genetic regulatory networks that
required only two essential enzymes. Knowing only how to implement
negatively regulated "genelets", we constructed a bistable feedback
circuit using two such genelets -- comprising six synthetic DNA
oligonucleotides. Here, we show how positive regulation can be
achieved, and build a single-switch positive feedback circuit that is
similarly bistable. With only four synthetic DNA oligonucleotides.
This simplicity encouraged us to characterize and model the system
within a Bayesian inference framework.
[ ACS Synthetic Biology:
ASAP version, June 26, 2012 (18 pages):
article, 4.1MB and
SI, 934KB.
]
[ Pre-submission rough draft on arXiv:
q-bio/1101.0723 (21 pages):
article, 1.4MB
under the name
Bistability of an In Vitro Synthetic Autoregulatory Switch.
]

Direct Atomic Force Microscopy Observation of DNA Tile Crystal Growth at the Single-Molecule Level.*Constantine Evans, Rizal Hariadi, and Erik Winfree.
It's nice to see what you're knowing. For over 15 years, our group
has been modeling DNA tile self-assembly as a crystal growth process
where individual tiles attach at a constant rate (independent of where
and how they attach) and detach at a rate that depends exponentially
on how many base pairs they are attached by. This model formed the
basis for our theoretical investigations, for our experimental
designs, and for our confidence that algorithmic self-assembly could
work with low error rates. We took it for granted. But we never
tested it directly. Now we have.
[ JACS134: 10485-10492, 2012 (8 pages, June 13):
article, 5.2MB and
supp. info. ]
[ Media: ChemistryViews. ]

Deterministic Function Computation with Chemical Reaction Networks.*Ho-Lin Chen, David Doty, and David Soloveichik.
Sometimes a little flexibility makes a huge difference. For example,
in Shannon's theory of information, the number of bits required to
specify an element of a set with no possibility of error (the
deterministic information) can be dramatically larger than the number of
bits required if you can tolerate some chance of error, no matter how
small (the probabilistic information). This work establishes a
perhaps even more dramatic distinction for computation within
well-mixed stochastic chemical reaction networks. Whereas it was
previously known that, accepting an arbitrarily small probability that
the output will be in error, well-mixed stochastic chemical reaction
networks can simulate Turing machines, and that in contrast questions
of reachability (rather than probability) are decidable, in this work
the exact class of functions that can be deterministically computed by
well-mixed stochastic chemical reaction networks (with no possibility
of error) is elegantly characterized in terms of semilinear functions. This is a huge gap!
[ Pre-publication draft on arXiv:
arXiv:1204.4176v1 (15 pages). ]
[ Accepted to the International Conference on DNA Computing and Molecular Programming 18, 2012. ]

Joseph's PhD Thesis:
Stochastic Simulation of the Kinetics of Multiple Interacting Nucleic Acid Strands.*
104 pages. California Institute of Technology. Submitted February 2013.
Joseph's MS Thesis:
The Multistrand Simulator: Stochastic Simulation of the Kinetics of Multiple Interacting DNA Strands.*
123 pages. California Institute of Technology. Submitted February 2012. Joseph Schaeffer. Thesis advisor: Erik Winfree.
Perhaps the central enabling concept for computer engineering is the
abstraction hierarchy: a tower of machine models that range from low
level details to high level concepts -- and that come with methods for
moving from one level to another with provable notions of equivalence.
DNA (and RNA) secondary structure kinetics will be near the bottom of
the stack for molecular programming, as it is currently envisioned.
In his PhD thesis (refined and improved from his Master's thesis),
Joseph takes important steps in defining the
model for multiple interacting strands, developing an efficient
simulator, and providing tools for analysis. This work should
provide a strong foundation for future efforts to build the
abstraction hierarchy for molecular programming.
[ PhD thesis, 4 MB;
Caltech ETD.]
[ MS thesis, 4 MB;
Caltech ETD.]
[ Multistrand is now publicly released; see the LNCS paper. ]

Parallelism and Time in Hierarchical Self-Assembly.*Ho-Lin Chen and David Doty.
The abstract Tile Assembly Model examines a single tile-based crystal
as it forms from a seed within an inexhaustible bath of free tiles.
But in solution, many crystals may grow in parallel, and if they
interact with each other by self-assembly, it is natural to think that
this parallelism could be exploited to grow well-defined structures
much more quickly. Somewhat remarkably, and counter-intuitively, the
authors show that if basic elements of chemical kinetics are taken
into account (low concentration species encounter each other less
frequently than high concentration species) then the parallelism of
hierarchical self-assembly provides no advantage at all
(caveat, caveat). If you want to build large complex things quickly, look
elsewhere.
[ Pre-publication draft on arXiv:
arXiv:1104.5226v1 (46 pages). ]
[
SODA 2012: Proceedings of the 23rd Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 1163-1182.article, 987 KB (20 pages). ]

Seung Woo's MS Thesis: Compiling and verifying DNA-based chemical reaction network implementations.*
120 pages. California Institute of Technology. Submitted September 2011. Seung Woo Shin. Thesis advisor: Erik Winfree.
Compilers are useless if the low-level implementation that they
produce as output is not semantically equivalent to the high-level
program that was provided as input. Proving a compiler's output to be
correct is an essential element of computer science -- and a
non-trivial one. Here, Seung Woo tackles this problem in molecular
programming, first building a general-purpose compiler for
implementing abstract chemical reaction networks using DNA strand
displacement cascades, then defining a notion of equivalence for
abstract chemical reaction networks, and finally providing a (usually)
efficient algorithm for testing whether a compiled network is correct
with respect to that notion. The results of testing on a number of
systems from the literature rather surprised me.
[ thesis, 1 MB;
Caltech ETD.
] [Tar archive of Nuskell, the CRN compiler and verifier: Seung Woo's thesis version.]

Timing molecular motion and production with a synthetic transcriptional clock.*Elisa Franco, Eike Friedrichs, Jongmin Kim, Ralf Jungmann, Richard Murray, Erik Winfree, and Friedrich C. Simmel.
The brilliance of genetic regulatory networks is that they are
programmable manufacturing plants. They can build all sorts of
things. Protein motors, self-assembling scaffolds, enzymes, ion
channels... they even build biochemical circuits, and transcription
factors that regulate what is built, and when. Can chemical engineers
learn to build non-biological molecular systems that operate according
to similarly powerful principles, as programmable molecular
manufacturing plants? As an exercise toward that goal, here we use
in vitro transcriptional systems -- a stripped-down model for
genetic regulatory networks in which RNA rather than protein plays the
important signalling and control roles, with only two essential enzymes
needed for RNA production and degradation -- to construct a
synthetic biochemical clock that controls downstream nucleic acid
machinery.
[ PNAS,
108: E784-E793, 2011
(10 pages): article, 9.7 MB,
summary, 1.7 MB,
supplementary information, 10.4 MB. ]
[ Highlighted in
Biopolymers,
reported by HFSP. ]

A simple DNA gate motif for synthesizing large-scale circuits.* 钱璐璐 (Lulu Qian) and Erik Winfree
What is the core of life? Is it, as the poets sometimes say, the ebb
and flow of the tides, the in and out of breathing, the ups and downs
of fortune? Or is it, as the electrical engineers might say, all in
the circuitry, the processing of information, the dynamics of
behavior? In this work, we present a simple DNA device, called the
"seesaw gate", that should make both poets and engineers happy. It
operates by a simple back-and-forth process -- a strand comes in on
one side, pushing that side "down" and kicking off the one on the other
side as it goes "up". And then visa versa, like a seesaw.
Released strands are then free to interact with other seesaw gates,
allowing networks to be designed systematically. Remarkably, the ebb
and flow of activity in these networks can perform computations of
arbitrary complexity in principle -- in fact, we describe a compiler
that translates digital logic circuits into functionally equivalent
seesaw gate networks, and we argue that the simplicity of the motif
should make networks containing thousands of gates possible. If this
theoretical proposal pans out experimentally, could it become a core
technology for embedding circuitry in synthetic biochemical systems?
[ DNA 14 conference preprint: (13 pages):
.pdf, 417 KB. ]
[ Conference version in LNCS 5347pages 70-89 (2009):
.pdf, 414 KB. ]
[ Journal version in Royal Society Interface8: 1281-1297 (2011):
article, 2.1 MB. ]

Synthetic in vitro transcriptional oscillators.*Jongmin Kim and Erik Winfree.
The first* purely chemical oscillator was discovered a little over 60
years ago. Belousov's detailed paper was rejected twice, appearing later
only as an abbreviated conference abstract and as a full paper only
posthumously. Thus ingloriously began the scientific study of how
chemical circuitry can lead to non-trivial dynamical behavior.
Eventually, of course, the study of simple chemical oscillators and
complex biological clocks flowered into a rich interdisciplinary
field. In this paper, we probe the middle ground by showing how
cell-free transcription and degradation can be systematically designed to
create a variety of oscillator architectures -- merging the
programmability of biology with the simplicity of in vitro reactions.
[ Molecular Systems Biology:
7: 465, 2011 (15 pages):
article, 2.6MB and
SI, 9.1MB and
models.zip, 2.8MB ]
*Leon Glass pointed out to me that Belousov's was not the first discovered. That credit appears to go to
W. C. Bray and A. L Caulkins circa 1921. Leon says he tried it, and it works. Thanks for the pointer, Leon!

Remote Toehold: A Mechanism for Flexible Control of DNA Hybridization Kinetics.*Anthony J. Genot, David Yu Zhang, Jonathan Bath, and Andrew J. Turberfield.
The concept of a "toehold" for initiating branch migration and strand
displacement has become central to our thinking about kinetic control
in DNA nanomachines and DNA circuits. Toeholds were originally
formulated as single-stranded extensions contiguous with the
double-stranded domain where branch migration occurs, so that a
complementary strand can bind to the toehold and initiate branch
migration up to six orders of magnitude faster than in the absense of
a toehold. Here, Genot and colleagues show that toeholds need not be
contiguous with the double-stranded branch migration domain;
localizing the invading strand at a remote site within the target
molecule can also serve to significantly accelerate the targeted
strand displacement reaction. The resulting design flexibility is
essential for some complex DNA nanomachines; furthermore, the
intervening region between the toehold and the branch migration domain
can be used as a knob to modulate the reaction rate. An idea worth knowing about.
[ JACS:
ASAP (6 pages):
article, 1.9MB and
SI, 600KB ]

Cooperative Hybridization of Oligonucleotides.*David Yu Zhang.
When two Watson-Crick oligonucleotides hybridize to each other, they
cancel each other out. This is useful. For example, it allows those
oligonucleotides to serve as opposing signals in their single-stranded
form. What if you want to build a DNA strand displacement circuit in
which two dynamic signals cancel each other out, but the two signals
must have unrelated sequences? Well, Dave's got an elegant trick for
you. And it gets better. When the signals cancel out, they also
release a new strand with a new sequence juxtaposition that can be fed
into downstream circuit components. He demonstrates these features by
constructing elegant Boolean logic gates and analog concentration
comparators. Even more useful!
[ JACS:
133: 1077-1086, 2011 (10 pages):
article, 2MB and
SI, 360KB ]

Elongational-flow-induced scission of DNA nanotubes in laminar flow.*Rizal F. Hariadi and Bernard Yurke.
Everyone knows what happens when an astronaut hops out of his
spaceship a little too close to a black hole. As he drifts toward the
black hole, the gravitational pull becomes stronger and stronger,
until it rips him apart, legs from his body, toes from his feet --
even molecules and atoms are eventually rent asunder. Interestingly, it's not
the magnitude of the gravitational force that is so disruptive, but
the change in gravity with distance, increasing as 1/R2. (An equally
strong, but constant, force would result in no worse than a relatively pleasant
free-fall sensation.) As it is, the astronaut's toes are eventually
pulled so much harder than his knees, that the differential force is
greater than the forces holding the tissue together -- and pop! Loosely
speaking, Rizal and Bernie have built a microfluidic black hole, and
rent asunder billions of DNA nanotube astronauts.
[ Physical Review E:
82: 046307, 2010 (11 pages):
.pdf, 1.6MB ]
[ Also enjoy this movie
of DNA nanotubes being compressed and stretched
as they enter and leave a side chamber that was accidentally created
in a defectively manufactured microfluidic channel.
This elongational flow is not sufficient to break the nanotubes. ]

DNA-based Fixed Gain Ampliﬁers and Linear Classiﬁer Circuits.* David Yu Zhang and Georg Seelig
It's great that an entropy-driven DNA catalyst can amplify a signal to detect the presence of a target nucleic acid molecule.
The amplified DNA signal can then trigger some downstream chemical activity, just under the right circumstances.
But what if the circumstance you're trying to detect isn't the presence or absence of a specific single species,
but rather a specific pattern of analog concentration levels for a spectrum of nucleic acid targets?
One option is to implement a threshold for each species, then process those YES/NO answers with digital logic -- AND and OR gates.
Another option, explored here, is to first implement analog logic that appropriately combines the signals from each species,
then takes a threshold to yield the final YES/NO answer. To do so, Dave and Georg propose a scheme for modifying our entropy-driven catalyst system
to serve as a signal multiplier, coupled with a mechanism for taking a difference and effecting a threshold.
The resulting neural network-like architecture could be quite handy for chemical pattern recognition.
[ DNA 16conference proceedings, 300 KB, 8 pages.
]
[
LNCS 6518pages 176-186, 2011:
.pdf, 275 KB.
]

Efficient Turing-universal computation with DNA polymers.* 钱璐璐 (Lulu Qian), David Soloveichik, and Erik Winfree
You've gotta love those little cartoons of Turing machines, you know, with the
robotic handcar
rolling along on the track writing zeros and ones all over the place?
It's a seminal model of abstract computing machines, sure, but real
computers aren't little motorized machines like toy trains. Right?
Computers don't even need moving parts -- just a smooth and soundless
flow of electrons through a staggering maze of wires carved into a
cold piece of silicon. The Turing machine model is great for
theorists, but of little use for anything else. Right? Wrong!
The Turing machine is a wonderful, practical, implementable model of
an autonomous molecular machine that modifies a linear heteropolymer.
Charles Bennett realized this many years ago during his studies of the thermodynamics of computing.
We don't quite figure out how to design a DNA Turing machine here, but
we get pretty close -- we give a theoretical construction for its
close cousin, the stack machine.
[ DNA 16conference proceedings, 600 KB, 14 pages. ]
[
LNCS 6518pages 123-140, 2011:
.pdf, 407 KB.
]

Simple Evolution of Complex Crystal Species.* Rebecca Schulman and Erik Winfree
How pervasive is the principle of evolution? How complex must be the
seed of life? Here we present our take on the simple origins of
complexity, extending Graham Cairns-Smith's ideas: that the logic
itself of crystallization can in principle give rise to unbounded
complexity in pattern formation -- with very simple crystal repeat
blocks, in very simple environments, and without any intrinsic
chemical or mechanical function. Perhaps life is logically inevitable.
[ DNA 16conference proceedings, 332 KB, 11 pages.]
[
LNCS 6518pages 147-161, 2011:
.pdf, 768 KB.
]

Molecular robots guided by prescriptive landscapes.* Kyle Lund, Anthony T. Manzo, Nadine Dabby, Nicole Michelotti, Alexander Johnson-Buck, Jeanette Nangreave, Steven Taylor,
裴仁军 (Renjun Pei),
Milan N. Stojanovic, Nils G. Walter, Erik Winfree, and 颜颢 (Hao Yan).
How small can a robot be? When I was in school, I built a small robot
by taking a remote-control car, adding some light sensors and bump
sensors, and installing a tiny on-board computer. I programmed it up
to scurry around following walls. Lots of fun. But while I played,
researchers in academia and industry were building pint-sized robots
that carried out collective tasks in distributed "swarms", or that
connected to each other in reconfigurable ways to form "meta-robots".
Researchers wanted to make the robots smaller and smaller, so that
they could have lots and lots of them, so that they could do more and
more interesting things. Some even began using silicon chip
fabrication techniques to build MEMS (microelectromechanical systems)
robots only millimeters on a side. Once you get that small, there's
not really much room for a CPU and memory, much less sensors and
motors! How can you program a robot -- or a swarm of robots -- when
each one has such limited capabilities? It's a deep and important
question. Fast forward to today. Can you make a robot from a
single molecule? Can a single molecule sense its environment, make
decisions, and take actions? The answer is a resounding yes!
But how? Our first baby steps -- born of Milan Stojanovic's seminal
work on "smart and agile" deoxyribozyme "spiders" -- are reported here
in a collaboration lead by Milan that involved chemical synthesis and
characterization at
Columbia,
atomic force microscopy at
Arizona State University,
and real-time single-molecule fluorescence microscopy at
Michigan State
University.
[Nature465:206-210, 2010(5 pages, pdf, 920 KB) and
supporting information (pdf, 9 MB).
(Also check out a lovely perspective piece in Nature, and a
Nature blog,
the NSF press release
with an interview of Milan, the Caltech press release,
a commentary at The Scientist
that includes a single-molecule fluorescence movie of spiders from the Walter lab,
Chemical & Engineering News,
Chemistry World,
Popular Science,
MIT Technology Review,
Physics World,
an excellent
Discover Magazine blog,
a blog,
comments from a Biophysical Society Meeting, a discussion of
boffinry,
and something I don't understand in German.
)]

DNA as a Universal Substrate for Chemical Kinetics.* David Soloveichik, Georg Seelig, and Erik Winfree
If chemistry is programmable, what's the programming language? Well,
there are many possibilities... but let's not go with a fad. For well
over one hundred years, chemists have been using the elegant and
refined mathematical language of mass action chemical kinetics.
Traditionally, it has been used descriptively, as a means of
describing chemical systems encountered in the real world. As
chemical engineers interested in programming chemistry, we wish to use
the language of chemical kinetics prescriptively, as a means of
describing the behaviors we aim to achieve. It's a rich language,
capable of expressing behaviors as varied and sophisticated as stable
attractors, oscillators, chaotic dynamics, signal processing and
computation -- but much of the evidence for this has come from
theoretical studies of chemical reaction networks that are possible in
principle, rather than from the study of real systems. That is, for
the past hundred years, many intriguing chemical reaction networks
existed only in a kind of theoretical dream world, with no physical
implementation known. Finally, here we show how any chemical reaction
network you dream up can be implemented using systems of DNA logic
gates, transforming chemical kinetics from a modeling language into a
programming language. Go ahead, make your dreams come true!
[ Full paper in PNAS,
107: 5393-5398, online March 4, 2010
(6 pages): .pdf, 850 KB and
supplementary information, 650 KB
and the Mathematica notebooks for
compiling CRNs into DNA gate schemes.
(To go all the way to DNA sequences you'll need some
sequence design tools.)
]
[ DNA 14conference preprint, revised: (10 pages):
.pdf, 508 KB.
Extended abstract in LNCS 5347pages 57-69 (2009):
.pdf, 582 KB. ]

Robustness and modularity properties of a non-covalent DNA catalytic reaction.*David Yu Zhang and Erik Winfree.
What makes a molecule tick? There's one way to find out: Poke it.
Prod it. Dave thoroughly harrassed his entropy-driven DNA catalyst
system and found out a lot that way. A few surprises: * The system is
exquisitely sensitive to mutations in the catalyst strand sequence,
but relatively insensitive to mutations in the fuel strand sequence. *
The system is almost unaffected by a high background of random
poly-{A,C,T} strands, but performance rapidly degrades with high
concentrations of random poly-{A,C,G,T} strands. These results can
be explained in terms of design features of the entropy-driven catalyst
system. You'll also find
information about modeling, leak reactions, poisoning reactions,
strand purity, 5'/3' orientation, and bulky add-ons to the catalyst.
The bottom line: this is stuff you'll want to know if you plan on
designing robust and modular strand displacement circuits.
[ Nucleic Acids Research:
38: 4182-4197, 2010 (16 pages):
.pdf, 1.8MB ]

Time-Complexity of Multilayered DNA Strand Displacement Circuits.* Georg Seelig and David Soloveichik
Of central importance in the theory of computation -- and in life in
general -- is how long it takes to get things done. For standard
models such as digital circuits and Turing machines, time complexity
is very well understood. Does our understanding of classical
computation directly yield results for computation in biochemical
circuits? Of course, it depends on how you do things. For example,
as shown here, circuits built from stochiometric gates (one output
molecule per input molecule) are asymptotically slower than those
using catalytic gates (each input molecule can produce many output
molecules). This suggests that the time complexity of formal chemical
reaction networks is likely to develop into an interesting, rich --
and probably suprising -- theory.
[ A preliminary extended abstract appears in DNA 15,
LNCS 5877pages 144-153, 2009:
.pdf, 451 KB.
]

Programmable Control of Nucleation for Algorithmic Self-Assembly.*Rebecca Schulman and Erik Winfree.
When writing a computer program, it is easy -- so trivial you don't
even think about it -- to make sure that your algorithm starts with
the correct input and proceeds from there. Models of algorithmic
self-assembly usually assume that assembly begins with a "seed tile"
which provides the input information. But molecular
self-assembly is an inherently parallel process; assembly begins anywhere
it is energetically favored. In this paper we show that
tile sets can be constructed that introduce arbitrarily large barriers
to spurious nucleation (starting self-assembly from something other
that the seed tile). By combining this construction with previous methods for
proofreading tile sets, we can now construct tile sets that are robust
to all major types of errors, without introducing significant slow-down.
Control of nucleation also
has some very interesting applications, such as enzyme-free detection
and amplification, and enzyme-free in-vitro evolution.
[ SIAM Journal on Computing 39 (4) pp. 1581-1616, December 4, 2009,
(36 pages) .pdf, 1.5 MB. ]
[ preprint cond-mat/0607317 on arXiv.org
(22 pages): .pdf, 728 KB. ]
[ extended abstract in DNA Computers 10,
LNCS volume 3384: 319-328, 2005,
(10 pages): .pdf, 176 KB. ]

Control of DNA Strand Displacement Kinetics Using Toehold Exchange.* David Yu Zhang and Erik Winfree.
Computer programs work by transferring control from one line of the
program to another. Many DNA programs work by transferring control
from one part of a molecule to another. That's what toehold exchange
does. It is an essential mechanism in many of our DNA strand
displacement circuits. Here we study the device physics of toehold
exchange and show that kinetics can be predicted remarkably accurately
from the thermodynamics of toehold binding. With this understanding,
we can make our DNA programs transition smoothly from step to step.
[ JACS,
131: 17303-17314, 2009
(12 pages): paper, 2.2 MB,
supplementary information, 200 KB, addendum, 46 KB.]
[ Erratum: In equation 9 on page 17311, there should be a factor of /RT in the exponent of the numerator. ]
[ Erratum: The flowchart approximation of Figure 8, derived on SI page 13, uses an "average" base pair energy of -1.4 kcal/mol at 25C, which is an underestimate.
The true value at 25 C should be -1.7 kcal/mol, and the formulas in the flowchart should be adjusted.
The value of -1.4 kcal/mol is a better value for "average" base pair energies at 37C, or for "somewhat weak" base pairs (say 70% A/T) at 25C,
in which case the original flowchart holds. ]

An Information-Bearing Seed for Nucleating Algorithmic Self-Assembly.* Robert D. Barish, Rebecca Schulman, Paul W. K. Rothemund, and Erik Winfree.
What is a seed? The tiny seed of a giant sequoia tree, sprouting
after the fire. The invisible seed of an idea, from which a thousand
possibilities grow. A crystal seed, determining the order of all that
grows from it. The seed of man and woman, carrying with it the future
of humanity. Clearly, it's important stuff. Why? The seed carries
the information, the creative part, the inspiration -- and what
follows is mere mechanism, the consequences, the algorithm. In this
work, we use DNA origami as a highly effective seed for growing DNA
tile crystals. Arbitrary information can be put on the seed; it
directs the growth of DNA crystals and determines their
morphology... much as a genome determines phenotype of an
organism... or even, as an idea creates the future.
[PNAS,
106: 6054-6059, 2009
(6 pages): .pdf, 1.7 MB,
supplementary information, 2.6 MB, and
appendix, 124 KB. ]
(Comments in the press:
Caltech Press Release,
New Scientist,
Foresight
)

Statistical Learning of Arbitrary Computable Classifiers.*David Soloveichik.
It's possible to learn. But there's a conundrum. If the thing you're
trying to learn is really complex, you'll need a really complex model.
That means you'll need a lot of data to distinguish between the good
models and the bad ones. Can you know when you've got enough data?
Remarkably, yes... most of the time. But not until you've seen the
data -- a distinction that explains why other researchers (with
different learning assumptions) have claimed that this is impossible.
[arXiv preprint: cs.LG/0806.3537v2
(5 pages): .pdf, 84 KB. ]

Dynamic Allosteric Control of Noncovalent DNA Catalysis Reactions.* David Yu Zhang and Erik Winfree.
"When you're hot, you're hot; when you're not, you're not."
Some find in that phrase solace for fickle fortune. Others see an engineering principle.
It's the ideal for a switchable catalyst: when it's ON,
it works full speed ahead, but when it's OFF, nothing doing. In this
paper, we design and demonstrate a modification of the catalyst for a
previously studied DNA hybrization reaction (Zhang et al 2007) that
can be turned ON and OFF by an exogenous DNA strand. This is
accomplished by designing the catalyst so that it has two
conformations -- switchable by the exogenous strand -- one of which
hides the toehold critical for initiating the catalytic reaction.
I can almost hear those poor DNA molecules' lament.
[JACS,
130:13921–13926, 2008
(6 pages): .pdf, 850 KB. ]

Programmability of Chemical Reaction Networks.* Matthew Cook, David Soloveichik, Erik Winfree, and Jehoshua
Bruck. So you'd like to program chemistry, would you? Well,
it's tough. Suppose you already had a handle on the molecular design
problem: "No problem," you say, "given a specification for a set of
chemical reaction equations, I can construct molecules that react
according to plan." Even that's not good enough, because there are limits
to what a system can do when the parts are bouncing around like a bag
of marbles. So, it's tough. But we can give you some hints. In this
paper, we compare stochastic chemical reaction networks to a variety
of known models of computation (including one of our eccentric
favorites, John Conway's FRACTRAN) and examine the limits of
computability. You'll meet molecular counts, probabilities, vector
addition systems, primitive recursive functions... and discover just
when you can and can't perform uniform computation with chemistry.
And all this is for well-mixed solutions with a fixed number of
chemical species -- if you want to include polymers and geometrical
structures, that's a whole other game. Maybe easier, actually.
[In Algorithmic Bioprocesses, Springer Berlin Heidelberg,
Eds. A. Condon, D. Harel, J. N. Kok, A. Salomaa, E. Winfree,
pp. 543-584 (937 KB) (2009).
Draft preprint (45 pages): .pdf, 824 KB. ]

Programming DNA Tube Circumferences.* Peng Yin, Rizal F. Hariadi, Sudheer Sahu, Harry M. T. Choi, Sung Ha Park, Thomas H. LaBean, John H. Reif.
To form a good crystal, must the monomer unit be a compact,
well-folded structure? Or can it be a floppy mess? Peng shows that
what's really important is the structure in the context of the
resulting crystal -- so yes, a monomer can be a floppy mess, and it's
still alright! This philosophy leads to the "single-stranded tile"
(SST) motif. Because each tile consists of just one strand with four
domains, each specifying connectivity in one of the four lattice
directions. This allows a straightforward programming of crystals
ribbons and tubes with specified width. Lovely.
[Science,
vol 321: 824-826, 2008
(3 pages): online .pdf, 240 KB.
(26 pages): online supplementary, 3.6 MB.
See the blurb at nanotechweb.org
and
Caltech's Press Release.
]

David's PhD Thesis: Molecules computing : self-assembled nanostructures, molecular automata, and chemical reaction networks.*
133 pages. California Institute of Technology, Defended May 2008. David Soloveichik. Thesis advisor: Erik Winfree.
We call it the song of the
little nightingale.
According to the text of the
Clauser Prize announcement,
this thesis
provides seminal contributions to the theory of molecular
computing, addressing fundamental questions like: Can we program
the self-assembly of complex molecular structures? How can the
behavior of molecular systems be made more robust to imperfections and
noise? How complex can chemical circuitry become? And, what are the
fundamental limits? That's a lovely song to sing.
[.pdf, 2.5 MB;
Caltech ETD.]

Error suppression mechanisms for DNA tile self-assembly and their simulation.* Kenichi Fujibayashi, David Yu Zhang, Erik Winfree, Satoshi Murata.
With the pieces floating all over the place, how can self-assembly be
restricted just to the active attachment sites where you want it? How
can you prevent the pieces from sticking to each other to soon? Well,
one possibility is to put a lock on their binding sites, and design
the active attachment sites (and no others!) to serve as a key. Here,
we present two possible implementations of this concept for the
algorithmic self-assembly of DNA tiles. They are analyzed by theory
and simulation; surprisingly, for our designs, locking both the input
and output sides of tiles provides substantially greater error
suppression than just locking one side.
[Natural Computing,
(on line, July 2008)
(24 pages): online .pdf, 3.4 MB. ]

Robust Stochastic Chemical Reaction Networks and Bounded Tau-Leaping.* David Soloveichik
Biology is robust. Step on it, squash it, zap it, shake it -- odds
are, it will just keep going. What makes biological systems so
robust, and what are the implications of this robustness? To study
this question, forget the arms and legs and blood and guts --
biological organisms are just chemistry, intricate networks of
chemical reactions. What's special about robust chemical reaction
networks? That should be a simpler question. In this paper, David
makes a surprising connection: robustness allows stochastic chemical
reaction networks to be simulated efficiently. In fact, this insight
leads to an elegant and fast algorithm for simulating stochastic
chemical reaction networks and even results in formal statements
limiting how fast a simulator could possibly be. The result provides a new
and fundamental framework for analyzing the efficiency of stochastic
simulation algorithms. The bottom line is, robustness doesn't only
make life easier for the organism, it makes life easier for those of
us studying the organism.
[
Journal of Computational Biology16(3): 501-522 (2009),
(22 pages): .pdf, 364 KB.
arXiv version, with corrections & additions: cs.CC/0803.1030
(29 pages): .pdf, 427 KB. ]

Engineering Entropy-Driven Reactions and Networks Catalyzed by DNA.* David Yu Zhang, Andrew J. Turberfield, Bernard Yurke, and Erik Winfree.
The entropy of the universe is always increasing. That sounds like a
force -- something that keeps increasing can push something else, can't
it? The problem, of course, is that using entropy to do work sounds like
trying to plow a field by herding stray cats -- it just ends in chaos.
But does it have to? Nope: chemists, in fact, are quite familiar with
entropy-driven reactions. In this paper, we show how to design systems
of DNA molecules with catalytic reactions that are driven by entropy.
And it doesn't end in chaos, far from it: we argue that our reactions
can be wired together into arbitrary analog or digital circuits, which
means they can process information and thus create order. So entropy can
drive the production of order? Yup. No wonder the universe is such a
beautiful place!
[Science,
318:1121-1125, 2007
(5 pages)
.pdf, 604k and
supplementary info, 640k.
(A labeling correction for Fig. 4.)
Chosen as an editor's choice;
also see Roy Bar-Ziv's excellent
Perspectives essay,
an interesting
commentary in The Scientist
and a nice
article
in The New Scientist.

Computation with Finite Stochastic Chemical Reaction Networks.* David Soloveichik, Matthew Cook, Erik Winfree, and Jehoshua Bruck.
Some people think of chemistry as a bag of colored marbles. Shake
really hard. When the marbles hit each other, they change colors,
according to rules. So there's a bit of structure, but it's a chaotic
mess -- at any given moment, it's anyone's guess what will happen
next. Can chemistry do computation, then? At least since
Jacob & Monod, and perhaps before, it has been generally recognized
that biochemical systems, such as genetic regulatory networks, can
operate much like electrical circuits -- the concentration of some
chemical species can carry an ON/OFF signal. Arbitrary digital
circuit logic can be performed. If enough marbles turn green, we'll
say the output was "1". Bennett even realized that if we string the
marbles together like a necklace of beads, then Turing-universal
computation can be performed. That's strictly more powerful,
theoretically, than digital circuits. What we show here is that
finite stochastic chemical reaction networks -- bags of marbles without
strings -- can also perform Turing-universal computation. Reasonably
quickly, too! This result holds if we accept some probability, no
matter how small, that the chemistry will produce the wrong
output... but remarkably, the result fails if we insist that the
chemistry always and without exception produces the correct output.
It pays to be tolerant, if even ever so slightly.
[Natural Computing,
(Volume 7, pages 615-633, 2008),
(19 pages): online .pdf, 690 KB or
Technical Report CaltechPARADISE:2007.ETR085
(19 pages): .pdf, 530 KB.
]

Rebecca's PhD Thesis: The Self-Replication and Evolution of DNA Crystals.*
133 pages. California Institute of Technology, Defended May 2007. Rebecca Schulman. Thesis advisor: Erik Winfree.
Few questions are so profound as that of life's origins. It may be
that the answer is not ours to know. But we can know how it
could have happened -- that is, we can ask "What chemical
systems have the capacity to self-replicate and evolve?" This too is
a profound question, and a rich one; it asks about the design space
for evolvable chemical systems, and there must be many many ways. A
good place to start, then, would be the simplest. In that spirit,
Rebecca's thesis examines how DNA tiles could be programmed to
faithfully copy information, spawn daughter crystals, mutate, grow
under selective pressures, and thus evolve in potentially complex
evolutionary landscapes. What is truly remarkable is how such a
simple chemical mechanism -- the selective sticking that underlies
tile-based self-assembly -- can exhibit so many profoundly life-like
characteristics. Perhaps the essence of life is not so hard to come
by, after all?
[.pdf, 3.1 MB;
Caltech ETD.]

Synthesis of crystals with a programmable kinetic barrier to nucleation.* Rebecca Schulman and Erik Winfree.
Rock candy is my favorite form of sugar. It sparkles with beautiful
flat facets. It's tasty. And it practically makes itself, growing right on
the stick -- almost as you watch! All you have to do is slowly cool a pot-full of
supersaturated hot sugar water. Ahh, the beauty of crystal growth. But
if the solid form is thermodynamically favorable (it is growing, after
all) why does it grow just on the stick, and not precipitate out of
solution everywhere? The answer, of course, is that there is a
kinetic barrier to nucleation: small crystals are more likely to melt
than to grow. But your stick had on it some pre-formed large crystals
(sugar grains) that were more likely to grow than to melt. Seed
crystals, we call them. They suck up all the sugar, and voila, big
beautiful rock candy! All goes to show: control over nucleation is
wonderful to have. But rock candy is just a metaphor. Control over
nucleation is critical for a whole slew of biological processes --
such as the growth of the cytoskeleton -- where a structure needs to
be built in the right place and at the right time, but nowhere else.
It's natural to think that control over nucleation will be key to
self-assembling molecular technologies as well. That's what our
paper is about. We design DNA tiles that crystallize into ribbons --
but there's a big kinetic barrier to nucleation unless we add a seed.
Hopefully, this mechanism for controlling nucleation can be used
as a general subroutine for programming complex crystal growth processes.
[PNAS,
(vol. 104, pp. 15236-15241, 2007)
(6 pages): .pdf, 429 KB and
supplementary information, 1.4 MB.
]

Reducing Facet Nucleation during Algorithmic Self-Assembly.* 陳和麟 (Ho-Lin Chen), Rebecca Schulman, Ashish Goel, Erik Winfree.
A single bit flip in the source code and the program won't compile. A
single mistake in calculating the digits of pi, and every subsequent
digit is garbage. This is what happens in brittle algorithms:
corrupted information gets used to compute more information, which is
thus corrupted, and the infection grows. Our initial efforts to embed
algorithmic logic into DNA self-assembly were brittle. A single DNA
tile that attached at the wrong site would utterly disrupt the
algorithmic pattern being formed. So we invented a way to design
"proofreading" tile sets that allowed a few errors to occur without
disrupting algorithmic growth. Unfortunately, our construction turned
out to still have problems when crystals grew with large facets -- it
did not suppress errors occurring from spontaneous nucleation of new
layers of tiles on the facets. A few years ago, Ho-Lin and Ashish
proposed an improved construction for DNA tile sets, which they call
"snaked proofreading" tile sets, that has excellent theoretical
properties in this regard. Here, Ho-Lin and Rebecca demonstrate
experimentally that the fundamental principle of the new construction
is sound: we can design tile sets that logically suppress nucleation
on facets. In effect, those nasty bit flips will now most of the time
just flip right back.
[Nano Letters,
(on-line
August 24, 2007) (7 pages):
.pdf, 653 KB and
supplementary information, 93
KB. ]

An autonomous polymerization motor powered by DNA hybridization.* Suvir Venkataraman, Robert M. Dirks, Paul W. K. Rothemund, Erik Winfree, Niles A. Pierce.
Can a DNA molecule walk? Can we design a molecular motor from scratch?
If so, how could it work? Consider macroscopic motors for a minute:
they come in all varieties, using all sorts of principles -- internal
combustion engines, steam engines, Wankel rotary engines, electric
motors, pneumatic motors, solenoids, rockets, jets... each best suited
to different tasks. The molecular world has similar diversity. In
biology, we see rotary motors like ATPase and the flagellar motor,
walking motors like kinesin, linear motors like RNA polymerase and the
ribosome, and waving motors like cilia. Not to mention muscle. Among
the most mind-bending are the polymerization motors of pathogenic
bacteria, such as Rickettsia and Listeria, that live inside eukaryotic
host cells. By displaying proteins that catalyze the polymerization
of the host cell's actin, these bacteria create a "comet tail" behind
them that pushes them forcefully through the cell and even into
neighboring cells. This was the motor principle targeted in our work,
which was lead by Niles' group. Perhaps most fascinating is that the DNA
polymers grow by insertion between the polymer tail and the DNA
catalyst strands anchored on the "surrogate bacterial cell". This
insertion takes place by a series of conformational rearrangements
without ever the two sides losing their strong attachment to each
other. Quite a dance!
[Nature Nanotechnology,
(vol. 2, pp. 490-494, 2007)
(5 pages): .pdf, 738 KB and
supplementary information, 581 KB.
]

How Crystals that Sense and Respond to Their Environment Could Evolve.* Rebecca Schulman and Erik Winfree.
In 1965, Graham Cairns-Smith proposed that the first (and simplest)
Darwinian entities were clay crystals, and that as they evolved to
reproduce faster and more robustly, they catalyzed organic
synthesis... and eventually their invented technology took over the
reins... and this "genetic takeover" resulted in us, their organic
brainchildren. Sounds crazy, doesn't it? Especially since crystal
evolution hasn't been demonstrated experimentally. Well, read his
books. In any case, a few years ago we realized that we might be able
to evolve our DNA crystals in the lab -- it's not clay, but the
principles might be similar. So we asked ourselves, what might be an
interesting selective pressure that our crystals could be subjected
to, so that evolution leads to increasing functional complexity? The
answer was quite surprising: without any novel chemistry or physics,
purely informational aspects of crystal growth are in principle
sufficient for a crystal to "intelligently" respond to the presence or
absence in the environment of material required for growth -- and
crystals containing information that enables them to respond more
adeptly will grow and reproduce faster. This is intriguing.
[Natural Computing,
(Volume 7, pages 219-237, 2008)
(19 pages): online .pdf, 485 KB or
(17 pages): preprint .pdf, 256 KB. ]

Combining Self-Healing and Proofreading in Self-Assembly.* David Soloveichik, Matthew Cook, Erik Winfree.
If you cut a crystal, does it bleed? Normally, you'd think not... but
algorithmic crystal growth has some surprisingly life-like
properties... so it makes you wonder. For example, there are crystal
monomer solutions that, depending on the information contained in a
seed crystal, can grow into any algorithmically describable shape --
much like a biological developmental program. But what if the growth
process is error-prone? What if the crystal suffers damage from a
hostile environment (i.e. you cut it)? Previous work showed that even
under such conditions (considered separately), algorithmic crystals
can grow and maintain their integrity. But different constructions
and different arguments were used in the two cases. Here, we
introduce a new construction and a new proof technique that shows that
both challenges can be met simultaneously! No blood.
[Natural Computing,
(Volume 7, pages 203-218, 2008)
(16 pages): online .pdf, 472 KB or
(12 pages): preprint .pdf, 310 KB. ]

Thermodynamic Analysis of Interacting Nucleic Acid Strands.* Robert M. Dirks, Justin S. Bois, Joseph M. Schaeffer, Erik Winfree, Niles A. Pierce.
If you're thinking about the molecular machines that may have
inhabited the RNA World in times gone by, if you're planning on
engineering a modern-day DNA World, or even if you're just curious,
you may want to know what happens when you toss a collection of
strands together in a test tube. Will they fold up? Into what
shapes? Will they interact? Form multi-stranded assemblies? With what
concentrations? For single strands, existing dynamic programming
algorithms can find the minimum-free-energy fold and even calculate
the partition function exactly, so that the probabilities of
alternative folds can be compared. (At least, with respect to the
standard nearest-neighbor model of secondary structure.) The
bimolecular case has also been tackled. Here, Niles & his boys lead
the charge to solve the full problem for any number of strands. An
exact solution, with fast algorithms, is provided. The math is
elegant, involving symmetry groups, convex optimization, and what seem
like remarkable "coincidences". Nice.
[SIAM Review,
vol. 49, pp 65-88, 2007
(24 pages): preprint .pdf, 653 KB. ]

Complexity of Self-Assembled Shapes.*David Soloveichik and Erik Winfree.
If you can effectively describe a shape -- e.g. write a computer program that draws it -- then
can the shape be self-assembled by spontaneous local processes from just a few kinds of pieces?
The answer may be "no" if you are concerned about the exact size of
the shape, but if it is only the form of the shape that matters, then
the answer is always "yes". In fact, the Kolmogorov complexity of a
shape provides upper and lower bounds for the number of tile types
necessary to self-assemble it (at some scale).
Proof of this result makes use of a construction for programmable
"blocks" that execute a Turing machine simulation to guide the growth
process, and introduces a new proof technique for establishing when
growth is independent of the order in which tiles are added.
This work suggests that scale plays the same role in self-assembly as does time in
computability: when you ignore it and just ask, "can it be done at
all?", then the theory becomes clean and elegant.
[SIAM Journal on Computing 36 (6) 1544-1569, 2007,
(26 pages) paper, 810 KB.]
[preprint cs.CC/0412096 on arXiv.org
(25 pages): .pdf, 488 KB.]
[extended abstract in DNA Computers 10,
LNCS volume 3384:344-354, 2005,
(10 pages): .pdf, 272 KB, color,
.pdf, 271 KB, B/W]

Jongmin's PhD Thesis: In vitro Synthetic Transcriptional Networks.*
118 pages. California Institute of Technology, Defended December 2006. Jongmin Kim. Thesis advisor: Erik Winfree. This thesis
describes presents a simplified architecture for designing and synthesizing arbitrary dynamics in in vitro biochemical networks. Inspired by neural networks and genetic regulatory networks, the in vitro systems make use of just RNA polymerase and RNases in addition to DNA constructs that define the network structure. Theory demonstrates that arbitrary dynamics can be synthesized in general, and experiments demonstrate individual switches as well as circuits that implement bistability and oscillation.
[.pdf, 18 MB;
Caltech ETD.]

Construction of an in vitro bistable circuit from synthetic transcriptional switches.* Jongmin Kim, Kristin S. White, Erik Winfree.
How simple can life be? To some, the answer to this question is a
small bungalow on Fiji, a hammock, and the sound of waves sloshing and
slurping against the sand. Others are more inclined to think about
the origin of life, about minimal organisms, about what it would take
to create life from scratch. Being broad-minded, we appreciate both
perspectives. While our research on the first aspect of the problem
is still in progress, this paper reports our efforts in the second
direction -- efforts to recreate, in simplified form, the
information-processing heart of cellular processes: genetic regulatory
networks. We do it in vitro using just DNA, RNA, and a small
handful of enzymes... though not without encountering a few challenges and surprises!
[Molecular Systems Biology,
2:68, 2006
(12 pages):
paper and
supplementary info;
also see Michael Simpson's excellent
News & Views essay.
Raw data is available from our Extra Supplementary Material page.
]

Enzyme-Free Nucleic Acid Logic Circuits.* Georg Seelig, David Soloveichik, David Yu Zhang, Erik Winfree.
It's a game of molecular dominoes. One falls, bumps
into the next, triggering its fall. Sometimes two separate cascades
converge on a single domino, and only when both hit at once does the
domino fall. Or maybe either input is enough. In fact, you can build
any kind of logic circuit out of dominoes. You can make a domino
cascade that multiplies binary numbers, if you want. It's fun. But
maybe not so deep scientifically, not so useful. But suppose you now
do the same thing with molecules, say DNA strands. Now you have a way
to embed logical control in chemistry, to sense and react to molecular
events. Now you're at the same frontier of molecular information
processing that biology has been exploiting and refining for almost 4
billion years. We're a bit behind in the game.
[Science,
314:1585-1588, 2006
(4 pages)
paper and
supplementary information;
also see Walter Fontana's excellent
Perspectives essay,
Udi Shapiro's
News and Views essay
in Nature Nanotechnology, a note in
Scientific American,
Caltech's Press Release,
or a
general-interest article we wrote for a Caltech newsletter (we all helped write it, even though they mistakenly only put my name on it).
]

Catalyzed Relaxation of a Metastable DNA Fuel.* Georg Seelig, Bernard Yurke, Erik Winfree.
DNA machines need fuel. Whether the machine is a motor, a manipulator, or a computer, if it is to be capable of driving a system to perform a periodic behavior -- and what respectable machine can't do that? -- then it needs fuel. ATP is an excellent fuel: small, high energy content, simple... but, how can we put it?... holding it requires small hands. Not even the rain has such small hands. So certainly not human-designed DNA machines, yet. So for DNA machines, we will make do with a bigger fuel -- but one that can be specifically targeted. That, more or less, was the motivation for this work.
(The original work pursuing this line of reasoning was Turberfield et al 2003 [ref 1] and further progress was made in "DNA Hybridization Catalysts and Catalyst Circuits" [ref 37, see below]. Here, we finally have a system that works quite nicely.)
{apologies to ee cummings}
[JACS,
128(37): 12211-12220, 2006
(5 pages): .pdf, 1.4 MB. ]

A DNA Superstructure-based Replicator without Product Inhibition.* David Yu Zhang and Bernard Yurke.
DNA replication, when one becomes two, marks the fundamental moment in
life. How simple can the machinery for replication be? Can it be
designed from scratch? Dave and Bernie present here a proposal for a
clock-work machine -- an information-bearing superstructure made
entirely of multi-base DNA building-block motifs -- that replicates
its overall structure when exposed to the proper sequence of raw
building blocks and fuel. So it's theoretically possible. This
throws down the gauntlet: Can an autonomous scheme be devised? Can a
simpler implementation be found, one practical enough for experimental
demonstration? Can a chemical self-replicator be rationally designed?
[Natural Computing5(2): 183-202, 2006
(20 pages): .pdf, 1.3 MB. ]

Folding DNA to create nanoscale shapes and patterns.* Paul W. K. Rothemund
Paul sends a swarm of staple strands to tie viral DNA in knots...thereby self-assembling 100 x 100 nm objects
with roughly 6 nm resolution from the 7 kilobase single-stranded genomic DNA of M13mp18.
Rectangles. Squares. Triangles. Stars. Even a smiley-face. About 50 billion copies of each, in a typical reaction,
and with very high yields. It works like magic.
We did some calculations... Paul's smiley faces constitute the most concentrated happiness ever experienced on earth.
Each spot in such a structure contains a unique address and can be addressed as such by DNA hybridization, allowing
one to "write" on the DNA origami objects. Words. Pictures. Snowflakes. A map of North and South America.
We did some more calculations... Paul probably made more maps than have ever been produced in the history of mankind
-- we're definitely talking quantity over quality here. The applications of this technology are likely to be
less whimsical. For example, it can be used as a "nanobreadboard" for attaching almost arbitrary nanometer-scale components,
and there are few other ways to obtain such precise control over the arrangement of components at this scale.
You'll never look at M13 phage DNA the same way again...
[Nature440, 297-302 (16 March 2006).
article, .pdf, 575 KB. News and View, .pdf, 300 KB.
Supplementary material: .pdf, part 1, 6.3 MB; .pdf, part 2, 193 KB.
Caltech's Press Release.
]

Self-Healing Tile Sets.* Erik Winfree.
Wandering in the dreamy fields of abstraction and metaphor,
I like to think of algorithmic self-assembly as a toy model of organismal development.
A tile set can direct the growth of an algorithmic pattern from a seed assembly
"in the same way" as genetic DNA directs the growth of a salamander from an egg.
Similar principles seem to be at work in both systems: information flow is essential,
sophisticated programming is possible, the physics and chemistry is messy but fault-tolerance
can be achieved. The adult salamander, however, can do something that has not previously
been shown in algorithmic self-assembly -- after losing its tail, the salamander can regrow a new one!
Perhaps more remarkable, actually, is the ability of almost all multicellular organisms to heal
severe wounds within their bodies.
In this paper I investigate a (somewhat) analogous issue for algorithmic self-assembly, and
show that self-healing tile sets are possible.
[in
Nanotechnology: Science and Computation,
pages 55-78, 2006.
Preprint (24 pages): .pdf, 431 KB.]
[Note, a one-page abstract of this work appeared in the FNANO 2005 conference proceedings.
Unfortunately, the 3x3 self-healing transformation in the figure shown there had an error in the boundary and seed tile blocks. EW 8/05]

Complexity of Compact Proofreading for Self-Assembled Patterns.* David Soloveichik and Erik Winfree.
Presumably, there is some cost for obtaining low error rates during
self-assembly. Maybe assembly must be slower. Or the same pattern
can be assembled more reliably, but using more tile types. Or the
pattern must be assembled at a larger scale. Or all of the above. In
fact, Chen and Goel (2005) proved that if you can accept "just a
little slower", "just a few more tiles", and "just a slightly larger
scale", then any self-assembled pattern can be made as reliable as you
want. But suppose you insist that the pattern remain at exactly the original
scale, as do Reif, Sahu, and Yin (2005) ? We give evidence that for
some patterns -- which we term "robust" -- it is still possible to do
arbitrarily strong proofreading with modest costs in speed and tile
set size, but for other patterns -- which we term "fragile" -- it is
not... at least, not with any proofreading scheme that uses a certain
kind of redundancy.
[Published in DNA Computing 11, LNCS 3892: 305-324 (2006): .pdf, 595 KB.]
[Preprint, typos corrected 3/29/2006 (20 pages): .pdf, 237 KB.]

Self-Replication and Evolution of DNA Crystals.* Rebecca Schulman and Erik Winfree.
What is the simplest physical system capable of extensive Darwinian evolution?
Such a system might be a candidate for the origin of life.
One would expect that it must have certain features:
it must be capable of of reproducing as an organism to
populate an environmental niche; of storing an unbounded amount of
information in its "genome"; of copying that information with low
error rates; and of expressing that information as a phenotype with
selective advantages or disadvantages.
Graham Cairns-Smith has argued, since the 1960's, that mineral
crystals (such as clays) provide the most compelling example of a
simple and abundant physical system capable of extensive Darwinian
evolution: Clay crystals can store information as a pattern of
inhomogeneities that are propagated from layer to layer, with few
errors; they can reproduce by random fragmentation; and they can
express a variety of morphological phenotypes.
To be blunt, he proposes that your
great-great-great-great-great-....-grandparent was a lump of clay. I
think he may be right. But the evidence is thin: to date, no one has
managed to catch clay in the act of replicating information or
evolving. In this paper, we propose using experimentally-tractable
DNA tile self-assembly to investigate how evolution could conceivably
work on information-bearing crystals.
Won the conference best paper award! (of 94 papers)
[ ECAL 2005, in
LNCS 3630:734-743, 2005.
Preprint (10 pages):
.pdf, 2.3 MB,
.ps, 9.3 MB. ]

The Computational Power of Benenson Automata.* David Soloveichik and Erik Winfree.
In a series of experimental papers, Benenson et al demonstrated how information
encoded in DNA can be processed autonomously by a molecular automaton consisting of a type IIS
restriction enzyme (FokI) and a collection of DNA "rule molecules". They constructed several
two-symbol, two-state finite state machines as well as several 4-input AND/NOT gates.
Ultimately, applications envisioned include diagnosis of mRNA and delivery of a theraputic molecule.
Here, we formalize the class of logical computations that can be performed by such systems
and show that, in our abstraction, the finite-input computations that can be performed by
Benenson automata can be exactly characterized by a connection to branching programs -- which
indicates that (if restriction enzymes slightly more powerful than FokI can be found) Benenson
automata are considerably more powerful than we had originally imagined!
[Preprint: cs.CC/0412097 on arXiv.org
(18 pages): .pdf, 223 KB.]
[Journal version: Theoretical Computer Science
244(2-3):279-297, 2005,
(19 pages): .pdf, 192 KB.
Erratum: .pdf, 279 KB.
]
[Note: Thanks to remarkably thorough comments from the reviewers,
the clarity and precision of the definitions and proofs in the journal version have been improved substantially.
Read this version, not the arxiv version!]

Algorithmic Self-Assembly of DNA Sierpinski Triangles.* Paul W. K. Rothemund, Nick Papadakis, Erik Winfree.
Our first demonstration of algorithmic crystals, wherein
molecularly-encoded information directs the growth process to create a complex pattern.
The DNA crystals are, at the molecular level, a two-dimensional woven fabric of short DNA strands.
Both because this programmable growth could be considered a super-simplified toy model of
organismal development, and because DNA is the central information molecule in biology,
I like to call it "weaving the tapestry of life".
This is a substantial personal victory for me: I proposed that this
should be possible in 1995 as a graduate student -- nearly 10 years
later, Paul's efforts made it actually happen.
[PLoS Biology 2 (12) e424, 2004,
(13 pages): .pdf, 4.6 MB.]
See also our Extra Supplementary Materials page.
(PLoS Biology has a
synopsis
and a
primer by Chengde Mao for this paper.
Also it was highlighted
in Nature by Philip Ball.
And there's a
Caltech Press Release.
)

Design and Characterization of Programmable DNA Nanotubes.* Paul W. K. Rothemund, Axel Ekani-Nkodo, Nick Papadakis, Ashish Kumar,
Deborah Kuchnir Fygenson, Erik Winfree.
DNA tiles designed to make sheets sometimes roll up into tubes that are abstractly analogous to
protein microtubules that self-assemble from tubulin. Way cool! Fortuitously discovered during
Paul's work on the DNA Sierpinski triangles, DNA nanotubes have opened up a whole host of
interesting possibilities that we never dreamed of before...
[JACS 126(50):16344-16353, 2004,
(9 pages): article, 891 KB,
supp, 5.5 MB.]
See also our Extra Supplementary Materials page.

[Note added Feb. 2013: We presented a correct equation for the persistence length of a DNA tube but gave an incorrect derivation. Here is the erratum stating
changes to the paper and the correction to the supplementary information
which gives a valid proof. Remember kids, area moment of inertia is for bending,
mass moment of inertia is for spinning ice skaters!]

Neural Network Computation by in vitro Transcriptional Circuits.* Jongmin Kim, John J. Hopfield, Erik Winfree.
Is it possible to design biochemical circuits in the same way we design electrical circuits --
where the information processing and dynamics is what we're interested in, rather than the
chemistry per se? What kinds of dynamical and decision-making behavior can be achieved this way?
In this paper, we give a concrete proposal for how to use synthetic DNA molecules and a few enzymes
(RNA polymerase and some ribonucleases) to make general-purpose threshold gates that can be wired
together to make arbitrary circuits. The mathematical description turns out to be closely related
to continuous-time analog neural networks. We analyze a few example circuits.
[Advances in Neural Information Processing Systems
(NIPS) 17, 2004, pg 681-688. preprint, (8 pages):
.pdf, 426 KB.]

DNA Hybridization Catalysts and Catalyst Circuits. *Georg Seelig and Bernard Yurke and Erik Winfree.
Energy stored in metastable configurations of DNA molecules can in
principle be used to power DNA nanomachines and other molecular
processes. Essential to using this energy productively is the ability
to regulate how and when the energy is released. Starting with a
previously-demonstrated DNA hybridization catalyst for doing exactly
that, we introduce schemes for an improved catalyst and for networks
of catalysts that operate as computing circuits. We show preliminary
experimental results investigating these proposals -- which uncover
a few interesting surprises!
[ in DNA Computers 10,
LNCS volume 3384:329-343, 2005,
(15 pages): .pdf, 361 KB ]

Proofreading Tile Sets: Error Correction for Algorithmic Self-Assembly.*Erik Winfree and Renat Bekbolatov.
Experimental studies of algorithmic self-assembly have observed error rates between 1 and 10 %,
measured as the fraction of DNA tiles that fail to perfectly match their neighbors. It is difficult
to perform extended computations when every elemental logical operation is so likely to be wrong.
Here, we provide a general-purpose technique for designing tile sets that are robust to assembly
errors. Kinetic and thermodynamic models of self-assembly are key to our investigations.
It is suggested that proofreading tile sets can square the error rate for comparable physical
conditions -- i.e. bring 10% to 1% and bring 1% to .01%.
[in DNA Computers 9,
LNCS volume 2943:126-144, 2004,
(19 pages, in color):
.pdf, 2.0 MB,
.ps, 18 MB]
See also our Extra Supplementary Material page.
[Note: Typo in Fig 7b: "FC" on the left should be "FM".]

Self-Assembled Circuit Patterns.*Matthew Cook, Paul W. K. Rothemund, and Erik Winfree.
Can DNA self-assembly be used for patterning, as a scaffold for functional devices such as
molecular electronic circuits? We show that several circuit patterns, including demultiplexers,
random-access memory, and Hadamard matrix transforms, can be self-assembled (in principle) from
a small number of tile types.
[in DNA Computers 9,
LNCS volume 2943:91-107, 2004.
(17 pages, in color):
.pdf, 608 KB,
.ps, 3.2 MB]

One Dimensional Boundaries for DNA Tile Self-Assembly.*Rebecca Schulman, Shaun Lee, Nick Papadakis, and Erik Winfree.
Discusses our progress toward using DNA tiles to self-assembly the boundary for
a self-assembled Sierpinski triangle. Experimental results show that individual tiles
behave well, with the expected tile-tile interactions, but size and shape distributions
of self-assembled structures were sometimes surprising and unsatisfactory.
We understand this by analyzing models of 1D polymerization, for example
distinguishing accretion from a seed vs. parallel aggregation. This work identifies control over
nucleation as an important target for future study in algorithmic self-assembly.
[in DNA Computers 9,
LNCS volume 2943:108-125, 2004,
(19 pages, in color):
.pdf, 2.1 MB,
.ps.gz, 8.7 MB,
.ps, 49 MB]
See also our Extra Supplementary Material page.

Protein Design is NP-Hard.*Niles Pierce and Erik Winfree.
Shows that a commonly-used formulation for
protein design -- amino acid sequence selection to stabilize a given
backbone fold using a pairwise energy model -- is NP-Hard if the
energy function is considered part of the specification of the problem
(as it is in common practice, since this is the implicit formulation
of the target backbone fold). Therefore, it may be advantageous to
exploit specific properties of protein folding energetics, rather than
relying on general-purpose (worst-case) exponential-time algorithms.
[in Protein Engineering, v15,
pp. 779-782, 2002 (4 pages):
PRODES.pdf, 1.1 MB]

Combinatorial Optimization Problems in Self Assembly.*Leonard Adleman, Qi Cheng, Ashish Goel, Ming-deh-Huang, David Kempe, Pablo Moisset, Paul Rothemund
Can one find the minimal number of tiles required to uniquely produce a given shape? Here we prove that
the problem is NP-complete. Also, for a large class of tile sets we give a method to find concentrations
of tiles that yield the fastest time of self-assembly.
[in STOC 2002, (10 pages):
.pdf, 731 KB,
.ps, 537 KB]

Paul's PhD Thesis: Theory and Experiments in Algorithmic Self-Assembly.*
283 pages, in black and white. University of Southern California, December 2001. Paul W. K. Rothemund. Thesis advisor: Leonard Adleman.
This thesis describes theory on the uniqueness of self-assembled structures with an expanded account of material in the
paper "The Program-Size Complexity of Self-Assembled Squares" (see below),
experiments in algorithmic capillary force-based self-assembly as well as capillary
force-based assembly of Penrose tilings,
and DNA computation for breaking the Data Encryption Standard (DES).
It has appendices detailing the frequency of
certain tile configurations (vertex stars) in the Penrose tiling
and an initial experiment in making capillary force-based gears.
[pwkr_thesis_nov15.ps, 49.8 MB, or
pwkr_thesis_nov15.ps.gz, 8.8 MB, or
pwkr_thesis_nov15.pdf, 9.1 MB]

Using lateral capillary forces to compute by self-assembly. * Paul W. K. Rothemund.
Here Paul used macroscopic plastic tiles to test ideas about algorithmic self-assembly. The
plastic tiles self-assemble at the interface of oil and water, and hydrophilic and hydrophobic
patches on the edges of the tiles mediate the specific binding interactions between them. Tiles in this
paper encode binding interactions for creating Sierpinski triangles as well as Penrose tilings. Paul had mild
success creating unnucleated patterns with Sierpinski tiles and perhaps created the most complex
set of specific capillary bonds ever made.
[in Proceedings of the National Academy of Sciences, 97(3): 984-989, 2000, (6 pages):
Rothemund-PNAS-capillary.pdf, 911KB]

A DNA and restriction enzyme implementation of Turing Machines.* Paul W. K. Rothemund.
Here Paul gives a construction for simulating Minsky's 4 symbol, 7 state universal
Turing machine using DNA, the type IIS restriction enzyme Fok I, and ligase.
The encoding of machine state and current symbol used in this paper was later used
by Kobi Benenson of Udi Shapiro's group to create DNA finite state machines and hence
such machines have been called Rothemund-Shapiro machines.
[in DNA Based Computers, pgs 75-120, 1996, (29 pages below):
dimacs.ps, 578KB, or
dimacs.pdf, 330KB]

Organizing Centers in a Cellular Excitable Medium.* Arthur T. Winfree, Erik M. Winfree, and Herbert Seifert.
Excitable media support directed wave propagation that, unlike
linear waves, are directed and self-sustaining but annihilate each
other when they collide. Examples include, in one dimension, action
potential propagation along a neuron; in two dimensions, a
slow-moving fire burning across a quick-growing plain of grass
leaving a thin zone of burnt grass in its wake; in three dimensions,
the electrical-contractile waves that make heart muscle beat. The
Belousov-Zhabotinski reaction provides a simple chemical analog in
any dimension, and the Greenberg-Hastings cellular automaton
provides a simple discrete model that exhibits many of the same
qualitative behaviors. The most striking behavior of excitable
media in two dimensions is that after part of a wavefront is rubbed
out, a spiral pattern develops as the wavefront swirls around its
end. In three dimensions, one observes a wavesheet rather than a
wavefront -- and if one rubs out a hole in that wavesheet, what
develops is a remarkable three dimensional spiral. In fact there
are an infinite variety of topologically distinct three dimensional
spirals, each corresponding to the Seifert surface of a distinct
knot. We simulated two such spirals in a three dimensional
Greenberg-Hastings cellular automaton.
[in
Physica 17D (1985), 109-115 (7 pages):
.pdf, 487KB.]
P.S. This is my first published work! My contribution, as a high
school student, was to write the program for simulating the cellular
automaton and visualizing initial conditions and the resulting three
dimensional pattern formation.